2012/2/22
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Osaka University
Analysis of the Collaboration Structure in Router-level Topologies
Yu Nakata∗, Shin’ichi Arakawa∗, and Masayuki Murata∗
∗Graduate School of Information Science and Technology
Osaka University, Japan
Osaka University
Contents
• Research Background
• Purpose and approach
• Numerical evaluation
• Confirmation
• Conclusion and future work
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Research Background
• The Internet becomes one of social infrastructures
• Reliability to survive against failures of network
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The Internet
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Reliability and Physical connection
• Physical connection of network is essential
• Investigation of relationships between characteristics and structures in networks
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Disconnect
Failed Failed
The Internet The Internet
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Transcriptional regulatory network [1]
Purpose and approach
• Approach
1. Using knowledge in biology
• Focus attention on
“transcriptional regulatory networks (TRNs)”
2. Comparing between router-level topologies and TRNs
3. Evaluation of a structure relating to reliability
• Collaboration structure
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Research physical structures for high reliable router-level topology
[1] M. Carro, et. al., “The transcriptional network for mesenchymal
transformation of brain tumours,“ Nature, Jan. 2010.
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Networks in living organisms
• The networks with long evolutionary history
• Many environmental changes
• Even if some components in the networks are broken, networks did not collapse
• The organism keeps alive
• Focus attention on transcriptional regulatory networks
• Deeply studied in the field of biology
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high robustness and adaptability
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Transcriptional regulatory networks (TRNs)
• TRNs are in a cell of organism
• Components
• Node : Transcription factors (TF)
• TF : protein
• Link : Transmission of signal
• Function
• To regulate proper genes in response to environmental stimuli
• Similarities to router-level topologies
• Information flow
• Hierarchical structure 7
Model of TRNs
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Analogy : Downward information flow
• Flow of regulation signal for expression
• Flow of traffic from backbone to access networks
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Backbone
Backbone
A module of AT&T topology
New Orleans in the USA
Top
Middle
Bottom
Environmental stimuli
Top
Middle
Bottom
TRNs Router-level topologies
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• Dividing the topologies into modules[2] in router-level topologies
• Module is a set of nodes in each region
TRNs
Analogy : Hierarchical structure
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[2] R. Guimera and L. A. N. Amaral, “Functional cartography of complex metabolic networks,”
Nature, vol. 433, p. 895, 2005.
Top level :
zero in-degree
Router-level
topologies
Top level : Nodes
having links that
connect with the other
modules
Middle level : in-degree
and out-degree
Middle level : in-degree
and out-degree
Bottom level :
zero out-degree
Bottom level :
zero out-degree
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Evaluation of reliability
• Which is more reliable, router-level topologies or TRNs?
• Investigating with a ratio of nodes which can receive signal from top-level nodes when there are failure nodes
• Index for investigating reliability
• Failure nodes :
• A ratio of failure nodes
• Reachable node ratio :
• A ratio of nodes which can receive signal from top-level nodes
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Evaluation of reliability
• Measure of reliability of both networks
• Calculate the number of nodes which can receive signal from top-level nodes
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T T
M M
M
B
M M
B
B
Randomly
Failed
T : Top
M : Middle
B : Bottom
Amount of failure nodes
Amount of nodes
reachable from top-level
Reliability
0
10
10/10
1
8
8/10
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Evaluation of reliability
• Measure of reliability of both networks
• Calculate the number of nodes which can receive signal from top-level nodes
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T T
M M
M
B
M M
B
B
Randomly
Failed Randomly
Failed
T : Top
M : Middle
B : Bottom
Amount of failure nodes
Amount of nodes
reachable from top-level
Reliability
1
8
8/10
2
6
6/10
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Result of evaluation for reliability
• Most TRNs are more reliable than ISP router-level topologies
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Router-level
topologies
TRNs Router-level
topologies
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Collaboration structure [3]
• A structure where multiple nodes connect with one node
• Leading multi paths → Contributing reliability
• Hierarchical structure
• Categorizing the topology into three layers
• top level, middle level and bottom level
• A key to identify the collaboration structure
• Where and how many collaboration structures are?
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[3] N. Bhardw aj, K.-K. Yan, and M. B. Gerstein, “Analysis of diverse regulatory netw orks in a hierarchical context show s consistent
tendencies for collaboration in the middle levels,” PNAS, vol. 107, pp. 6841–6846, Mar. 2010.
(B , D), (B, E) and (E, F) contribute
collaboration structure respectively.
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• Three types of collaboration structure
• Classify collaboration structure
• Degree of collaboration 𝐷𝑐𝑜𝑙𝑙𝑎𝑏𝐿1,𝐿2
• Amount of collaboration structure of 𝐿1 level and 𝐿2 level
• Example :
Definition of collaboration
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𝐷𝑐𝑜𝑙𝑙𝑎𝑏𝑚𝑖𝑑𝑑𝑙𝑒,𝑡𝑜𝑝
=𝑆𝑚𝑖𝑑𝑑𝑙𝑒 ∩ 𝑆𝑡𝑜𝑝
𝑆𝑚𝑖𝑑𝑑𝑙𝑒 ∪ 𝑆𝑡𝑜𝑝
𝑆𝑚𝑖𝑑𝑑𝑙𝑒：A set of nodes regulated by
nodes in middle level
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Degree of collaboration
• Example：Degree of collaboration 𝐷𝑐𝑜𝑙𝑙𝑎𝑏
• Degree of collaboration reflects amount of collaboration structures in networks
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𝐷𝑐𝑜𝑙𝑙𝑎𝑏𝑡𝑜𝑝,𝑚𝑖𝑑𝑑𝑙𝑒
=1
6 𝐷𝑐𝑜𝑙𝑙𝑎𝑏
𝑡𝑜𝑝,𝑚𝑖𝑑𝑑𝑙𝑒=
4
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Calculation result of degree of collaboration
• Degree of collaboration of top-level node and middle-level node is low in router-level topologies
• Expectation : Collaboration structure of top level and middle level contributes reliability
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Degree of collaboration of
top-level and middle-level is
much lower than other
degree of collaboration in
router-level topologies TRNs Router-level topologies
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Degree of collaboration and reliability
• Confirmation of correlation between collaboration structure and reliability by means of rewiring operation
• To increase degree of collaboration of top-level and middle-level in router-level topologies
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Rewiring Pattern A Rewiring Pattern B
X
Y
Z X
Y
Z
Step. 1 Node X is regulated by three or
more nodes included in the same layer.
Step. 2 Node Y is one of
nodes regulating Node X.
Step. 3 Node Z is regulated by
only nodes in one layer.
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Degree of collaboration after rewiring
• Calculating degree of collaboration after rewiring
• Degree of collaboration of top-level and middle-level increased in router-level topologies
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Before rewiring After rewiring
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Change of reliability in router-level topologies
• Reliability of router-level topologies before and after rewiring
• Reliability was improved in all topologies
• AT&T, Ebone, Exodus, Level3, Sprint, Telstra, Tiscali, Verrio
20 Telstra Tiscali
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Conclusion and future work
• Conclusion
• Degree of collaboration of top-level node and middle-level node in router-level topologies is lower than TRNs
• Collaboration structures of top-level and middle-level contribute reliability
• Future work
• Investigating why there is difference of improvement of reliability depending on router-level topologies after rewiring
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